Computational Analysis of Musical Structures Based on Morphological Filters

Abstract

This paper deals with the computational analysis of musical structures by focusing on the use of morphological filters. We first propose to generalize the notion of melodic contour to a chord sequence with the chord contour, representing some formal intervallic relations between two given chords. By defining a semi-metric, we compute the self-distance matrix of a chord contour sequence. This method allows generating a self-distance matrix for symbolic music representations. Self-distance matrices are used in the analysis of musical structures because blocks around the diagonal provide structural information on a musical piece. The main contribution of this paper comes from the analysis of these matrices based on mathematical morphology. Morphological filters are used to homogenize and detect regions in the self-distance matrices. Specifically, the opening operation has been successfully applied to reveal the blocks around the diagonal because it removes small details such as high local values and reduces all blocks around the diagonal to a zero value. Moreover, by varying the size of the morphological filter, it is possible to detect musical structures at different scales. A large opening filter identifies the main global parts of the piece, while a smaller one finds shorter musical sections. We discuss some examples that demonstrate the usefulness of this approach to detect the structures of a musical piece and its novelty within the field of symbolic music information research.